### Abstract

The Optical Multi-Trees (OMULT) is an interconnection network proposed by Sinha and Bandyopadhyay [B.P. Sinha, S. Bandyopadhyay, OMULT: An optical interconnection system for parallel computing, Lecture notes in Computer Science 3149 (2004) 302-312], for optoelectronic parallel computers. Various algorithms including matrix multiplication, DFT computation, sorting, prefix sum have been successfully mapped on this architecture. In this paper, we develop efficient parallel algorithms for some commonly used permutations namely, bit reversal, vector reversal, perfect shuffle, unshuffle and transpose on the OMULT network. Our algorithm for bit reversal permutation requires 8 log n electronic moves +7 optical moves for n^{2} data elements and O (n) electronic moves +3 optical moves for n^{3} data elements; the vector reversal for n^{3} data elements requires 3 g (n) electronic moves +4 optical moves, where g (n) is the time for local vector reversal on n data elements; the perfect shuffle for n^{3} data elements requires (3 f (n) + 8) electronic moves +8 optical moves, where f (n) is the time for local perfect shuffle on n data elements, and the transpose for n^{3} data elements runs in at most three optical moves, all using 2 n^{3}-n^{2} processors.

Original language | English |
---|---|

Pages (from-to) | 2656-2665 |

Number of pages | 10 |

Journal | Computers and Mathematics with Applications |

Volume | 56 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1 Nov 2008 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bit reversal
- Optical multi-trees
- Optoelectronic computer
- Permutation routing
- Shuffle
- Transpose
- Vector reversal

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Modelling and Simulation
- Computational Mathematics

### Cite this

*Computers and Mathematics with Applications*,

*56*(10), 2656-2665. https://doi.org/10.1016/j.camwa.2008.03.060

**Permutation algorithms on optical multi-trees.** / Jana, Prasanta K.; Sinha, Koushik.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 56, no. 10, pp. 2656-2665. https://doi.org/10.1016/j.camwa.2008.03.060

}

TY - JOUR

T1 - Permutation algorithms on optical multi-trees

AU - Jana, Prasanta K.

AU - Sinha, Koushik

PY - 2008/11/1

Y1 - 2008/11/1

N2 - The Optical Multi-Trees (OMULT) is an interconnection network proposed by Sinha and Bandyopadhyay [B.P. Sinha, S. Bandyopadhyay, OMULT: An optical interconnection system for parallel computing, Lecture notes in Computer Science 3149 (2004) 302-312], for optoelectronic parallel computers. Various algorithms including matrix multiplication, DFT computation, sorting, prefix sum have been successfully mapped on this architecture. In this paper, we develop efficient parallel algorithms for some commonly used permutations namely, bit reversal, vector reversal, perfect shuffle, unshuffle and transpose on the OMULT network. Our algorithm for bit reversal permutation requires 8 log n electronic moves +7 optical moves for n2 data elements and O (n) electronic moves +3 optical moves for n3 data elements; the vector reversal for n3 data elements requires 3 g (n) electronic moves +4 optical moves, where g (n) is the time for local vector reversal on n data elements; the perfect shuffle for n3 data elements requires (3 f (n) + 8) electronic moves +8 optical moves, where f (n) is the time for local perfect shuffle on n data elements, and the transpose for n3 data elements runs in at most three optical moves, all using 2 n3-n2 processors.

AB - The Optical Multi-Trees (OMULT) is an interconnection network proposed by Sinha and Bandyopadhyay [B.P. Sinha, S. Bandyopadhyay, OMULT: An optical interconnection system for parallel computing, Lecture notes in Computer Science 3149 (2004) 302-312], for optoelectronic parallel computers. Various algorithms including matrix multiplication, DFT computation, sorting, prefix sum have been successfully mapped on this architecture. In this paper, we develop efficient parallel algorithms for some commonly used permutations namely, bit reversal, vector reversal, perfect shuffle, unshuffle and transpose on the OMULT network. Our algorithm for bit reversal permutation requires 8 log n electronic moves +7 optical moves for n2 data elements and O (n) electronic moves +3 optical moves for n3 data elements; the vector reversal for n3 data elements requires 3 g (n) electronic moves +4 optical moves, where g (n) is the time for local vector reversal on n data elements; the perfect shuffle for n3 data elements requires (3 f (n) + 8) electronic moves +8 optical moves, where f (n) is the time for local perfect shuffle on n data elements, and the transpose for n3 data elements runs in at most three optical moves, all using 2 n3-n2 processors.

KW - Bit reversal

KW - Optical multi-trees

KW - Optoelectronic computer

KW - Permutation routing

KW - Shuffle

KW - Transpose

KW - Vector reversal

UR - http://www.scopus.com/inward/record.url?scp=53049087691&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=53049087691&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2008.03.060

DO - 10.1016/j.camwa.2008.03.060

M3 - Article

VL - 56

SP - 2656

EP - 2665

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 10

ER -